Average Shadowing Research Articles

Average shadowing and gluing property

AbstractThe purpose of this work is threefold: (i) extend shadowing theory for discontinuous and non‐invertible systems, (ii) consider more general classes of perturbations (for example, small only on average), (iii) establish a general theory based on the property that the shadowing holds for the case of a single perturbation. The “gluing” construction used in the analysis of the last property turns out to be the key point of this theory.

Performance Analysis of NOMA-Based Hybrid Satellite-Terrestrial Relay System Using mmWave Technology

This paper investigates the performance of NOMA-based hybrid Satellite-Terrestrial relays system (HSTR) using the millimeter wave (mmWave) technology. Furthermore, the relays are equipped with multiple antennas and utilize the amplify and forward (AF) protocol to forward the satellite’s superimposed information to multiple destinations. Then, the rain coefficient is considered as the fading factor of the mmWave band to choose the best relay. We considered the shadowed-Rician fading and Nakagami-m fading for satellite links and terrestrial links respectively, and in addition, we evaluated the shadowing effect for satellite links with two modes of: frequent heavy shadowing (FHS) and average shadowing (AS). With these suggestions, the closed-form outage probability (OP) and approximate ergodic capacity (EC) are derived to evaluate the efficiency of the proposed system. Next contribution of the research is an asymptotic analysis for the OP, which is derived in order to gain additional insight into important system parameters. Finally, the theoretical derivation is validated through simulation results and analyzed the impact of significant parameters. These results demonstrate NOMA’s superiority to the traditional orthogonal multiple access (OMA) method in the proposed system.

Selective PNC in satellite-terrestrial network over non-identical fading channels

We analyze the performance of a twoway satellite-terrestrial decode-and-forward (DF) relay network over non-identical fading channels. In particular, selective physical-layer network coding (SPNC) is employed in the proposed network to improve the average end-to-end throughput performance. More specifically, by assuming that the DF relay performs instantaneous throughput comparisons before performing corresponding protocols, we derive the expressions of system instantaneous bit-error-rate (BER), instantaneous end-to-end throughput, average end-to-end throughput, single node detection (SND) occurrence probability and average end-to-end BER over non-identical fading channels. Finally, theoretical analyses and Monte Carlo simulation results are presented. Evaluations show that: 1) SPNC protocol outperforms the conventional physical-layer network coding (PNC) protocol in infrequent light shadowing (ILS), average shadowing (AS) and frequent heavy shadowing (FHS) Shadowed-Rician fading channels. 2) As the satellite-relay channel fading gets more severe, SPNC protocol can achieve more performance improvement than PNC protocol and the occurrence probability of SND protocol increases progressively. 3) The occurrence probability increase of SND has a beneficial effect on the average end-to-end throughput in low signal-to-noise ratio (SNR) regime, while the occurrence probability decrease of SND has a beneficial effect on the average end-to-end BER in high-SNR regime.

Chaos and Shadowing in General Systems

In this paper we describe some basic notions of topological dynamical systems for maps of type f : X × X → X named general systems. This is proved that every uniformly expansive general system has the shadowing property and every uniformly contractive general system has the (asymptotic) average shadowing and shadowing properties. In the rest, Devaney chaos for general systems is considered. Also, we show that topological transitivity and density of periodic points of a general systems imply topological ergodicity. We also obtain some results on the topological mixing and sensitivity for general systems.

The Research of Asymptotic Average Shadowing Property and Pointwise Lipschitz Shadowing Property

We investigated the dynamical relationship between asymptotic average shadow ing property and pointwise Lipschitz shadowing property on the sequence map and the limit map. Then, we have: (1)Suppose {gn } strongly uniformly converge to g · gn has asymptotic average shadowing property implies g has asymptotic average shadowing property. (2) Suppose {gn } strongly uniformly converge to g · gn has fine pointwise shadowing property implies g has pointwise Lipschitz shadowing property. The above results promote the theory development of asymptotic average shadowing property and pointwise Lipschitz shadowing property.

Performance Analysis of Two-Way Satellite-Terrestrial Relay Network with SWIPT.

In this paper, we investigated the performance of a two-way satellite-terrestrial DF relay network with asymmetric simultaneous wireless information and power transfer (SWIPT). In particular, selective physical-layer network coding (SPNC) was employed in the proposed network, improving the throughput performance. We derived the expressions of system average end-to-end throughput and single node detection (SND) occurrence probability. Furthermore, to observe the effects of the power splitting (PS) coefficient on the energy efficiency performance, the expressions of energy harvested in the physical-layer network coding (PNC) and SPNC protocol were also derived. Finally, theoretical analyses and Monte Carlo simulation results are presented to show: (i) SPNC protocol outperforms the conventional PNC protocol in the two-way satellite-terrestrial relay network with SWIPT in infrequent light shadowing (ILS), average shadowing (AS), and frequent heavy shadowing (FHS) Shadowed-Rician fading channels; (ii) as the channel state gets worse, SPNC protocol can achieve more performance improvement than PNC protocol; (iii) as the PS coefficient increases, the average end-to-end throughput performance increases progressively, and the average energy efficiency performance increases progressively within a certain range, while decreasing in the others.

Average shadowing and persistence in pointwise dynamics

We introduce average shadowable measures and almost average shadowable measures for continuous maps of compact metric spaces and weakly topologically stable points and average persistent property for homeomorphisms of compact metric spaces. We prove that the set of all average shadowable measures is dense in the space of all Borel probability measures if and only if the set of all average shadowable points is dense in the phase space and every almost average shadowable measure can be weak⁎ approximated by measures having support equal to the closure of the set of all average shadowable points. Moreover, we prove that every minimally expansive point which is either persistent or α-persistent is weakly topologically stable and every mean equicontinuous pointwise weakly topologically stable homeomorphism is average persistent.

Limit Average Shadowing and Dominated Splitting

Limit Average Shadowing and Dominated Splitting

Outage Behaviors of NOMA-Based Satellite Network Over Shadowed-Rician Fading Channels

This paper investigates the application of non-orthogonal multiple access (NOMA) to satellite communication network over Shadowed-Rician fading channels. The impact of imperfect successive interference cancellation (ipSIC) on NOMA-based satellite network is taken into consideration from the perspective of practical scenarios. We first derive new exact expressions of outage probability for the p-th terrestrial user and provide the corresponding asymptotic analysis results. The diversity order of zero and p are achieved by the p-th terrestrial user with ipSIC and perfect successive interference cancellation (pSIC), respectively. Finally, the presented simulation results show that: 1) On the condition of pSIC, the outage behaviors of NOMA-based satellite network are superior to that of orthogonal multiple access; 2) With the value of residual interference increasing, the outage performance of terrestrial users with ipSIC is becoming worse seriously; and 3) Infrequent light shadowing of Shadowed-Rician fading brings the better outage probability compared to frequent heavy and average shadowing.

A unified approach to modelling of probability of detection over [formula omitted]-[formula omitted]/IG, [formula omitted]-[formula omitted]/IG, and [formula omitted]-[formula omitted]/IG composite fading channels with application to co-operative system

In this paper, the performance analysis of the energy detector based on the three composite fading channels such as α-μ/IG, η-μ/IG,and κ-μ/IG is investigated. First, a unified probability distribution function (PDF) of the three composite fading channels is developed based on Gauss-Laguerre integration and is expressed in the form of the mixture of IG distributions. Subsequently, the PDF is used for deriving the analytical forms of the average probability of detection (PD) along with the upper bound of the truncation error, optimization of the energy detection threshold, and the average area under receiver operating characteristic curve (AUC). Moreover, the simplified closed-form asymptotic expressions of the PD and the average AUC are also derived. Finally, the derived result is utilized to assess the performance of the cooperative spectrum sensing (CSS) under the various practical channel conditions such as infrequent light shadowing, average shadowing, and frequent heavy shadowing. Optimization of the threshold parameter and total number of cognitive radios utilizing n-out-of-M voting rule for CSS by minimising the total error rate (TER) is carried out. The accuracy of the derived analytical expressions has been corroborated with Monte-Carlo simulation and exact numerical results.

New Analytical Expressions for ASEP of Modulation Techniques with Diversity Over Lognormal Fading Channels with Application to Interference-Limited Environment

In this paper, the analytical expressions of the average symbol error probability (ASEP) for both coherent and non-coherent modulation formats with diversity schemes such as maximal ratio combining (MRC), equal-gain combining (EGC), and selection combining (SC) over the lognormal (LN) distribution assuming independent and identically distributed (i.i.d.) channels have been derived. The functions involving LN distribution are simplified using the Gauss–Hermit and Gaussian Quadrature integration. Furthermore, the effect of the diversity order and constellation size on the error probability has been examined extensively under various shadowing conditions such as infrequent light, average, and frequent heavy shadowing. As an application, the derived results are used to analyze the performance of the communication systems over the interference-limited environment. The impact of the number of interferers on important performance metrics such as the outage probability, the ASEP, and the channel capacity has been examined. The accuracy of the analytical results are validated by comparing them with the exact numerical results and Monte Carlo simulations. The analytical expressions are simple and easily implementable in software package such as MATLAB. The proposed analytical expressions are supposed to be a vital tool in areas such as IEEE 802.15.3a wireless communication system, indoor environment, radio channel effect by body worn devices, ultra-wideband indoor channel.

VARIOUS SHADOWING PROPERTIES FOR INVERSE LIMIT SYSTEMS

Let <TEX>$f:X{\rightarrow}X$</TEX> be a continuous surjection of a compact metric space and let (<TEX>$X_f,{\tilde{f}}$</TEX>) be the inverse limit of a continuous surjection f on X. We show that for a continuous surjective map f, if f has the asymptotic average, the average shadowing, the ergodic shadowing property then <TEX>${\tilde{f}}$</TEX> is topologically transitive.

On various definitions of shadowing with average error in tracing

When computing a trajectory of a dynamical system, influence of noise can lead to large perturbations which can appear, however, with small probability. Then when calculating approximate trajectories, it makes sense to consider errors small on average, since controlling them in each iteration may be impossible. Demand to relate approximate trajectories with genuine orbits leads to various notions of shadowing (on average) which we consider in the paper. As the main tools in our studies we provide a few equivalent characterizations of the average shadowing property, which also partly apply to other notions of shadowing. We prove that almost specification on the whole space induces this property on the measure center which in turn implies the average shadowing property. Finally, we study connections among sensitivity, transitivity, equicontinuity and (average) shadowing.

Partial shadowing of average-pseudo-orbits

The aim of this paper is to introduce and study $\underline{q}$-average shadowing. A map $f$ has $\underline{q}$-average shadowing property if for any $\varepsilon >0$, there is $\delta >0$, such that any $\delta$-average pseudo-orbit of $f$ can be $\varepsilon$-shadowed by some point along a set with lower density greater than $q$. We prove that the map $f$ has average shadowing property if and only if it has the $\underline{q}$-average shadowing property for any $q\in [0,1)$. We illustrate a map which has $\underline{p}$-average shadowing property for some $p\in [0,1)$ but without average shadowing property. In addition, we discuss the other dynamics properties of the $\underline{q}$-average shadowing property and its applications.

On homeomorphisms with the two-sided limit shadowing property

We prove that the two-sided limit shadowing property is among the strongest known notions of pseudo-orbit tracing. It implies shadowing, average shadowing, asymptotic average shadowing and specification properties. We also introduce a weaker notion that is called two-sided limit shadowing with a gap and prove that it implies shadowing and transitivity. We show that those two properties allow to characterize topological transitivity and mixing in a class of expansive homeomorphisms and hence they characterize transitive (mixing) shifts of finite type.

Average Shadowing, Asymptotic Average Shadowing and Dominated Splitting for Conservative Systems

Average Shadowing, Asymptotic Average Shadowing and Dominated Splitting for Conservative Systems

Diversity with distributed decisions combining for direct-sequence CDMA in a shadowed Rician-fading land-mobile satellite channel

The performance of two diversity schemes with distributed decisions combining is analyzed and compared with that of the selection and maximal ratio-combining schemes for binary-phase shift keying (BPSK) direct-sequence code-division multiple access (DS-CDMA) in a shadowed Rician-fading land-mobile satellite channel. In the first scheme of distributed decisions combining, the combiner collects only the binary branch decisions to make the data decision. In the second scheme, the combiner makes the data decision using the branch decisions and the channel states. Both symmetrical and asymmetrical diversity branches are considered. Based on optimal likelihood ratio testing, a new data decision rule is devised for the detection of the spread-spectrum signals in the DS-CDMA system. Upper bounds are employed for the performance evaluation of the diversity combining schemes when the bit error probability is difficult to compute. Numerical results are presented for the satellite channel under light, average, and heavy shadowing.

Diversity for noncoherent DPSK direct-sequence CDMA over a shadowed Rician-fading satellite channel

Spatial-diversity schemes with distributed detection combining are analysed and compared with selection and maximal-ratio for noncoherent DPSK direct-sequence CDMA (DS-CDMA) in a shadowed Rician-fading land-mobile satellite channel. To evaluate the performance of the distributed-detection combining scheme, the Chernoff upper bound on its bit error probability is employed. In the distributed-detection combining system, two schemes are considered. In the first scheme, each branch sends its temporary decision to the combiner in which the demodulated signals of individual diversity branches are independent. In the second scheme, the demodulated signals are independent when conditioned on the channel state, and the combiner collects the detection results of the branches with the channel state information. Numerical results are presented for performance comparisons between the distributed detection, selection and maximal ratio combining for the DPSK DS-CDMA under light, average and heavy shadowing.

A model for seasonal and annual cooling tower impacts

The Argonne National Laboratory/University of Illinois Seasonal/Annual Cooling Tower Impacts model provides predictions of seasonal, monthly, and annual cooling tower impacts from any number of mechanical- or natural-draft cooling towers. The model typically requires five years of hourly surface meteorological data and concurrent twice-daily mixing heights in addition to basic data on the thermal performance of the cooling tower. The model predicts average plume length, rise, drift deposition, fogging, icing, and shadowing. The model uses a category scheme in which the five years of hourly surface data are placed into about 100 categories based on a special plume-scalling relationship. With this reduced number of cases to be run for long-term impact evaluations, advanced state-of-the-art models for plume impacts are then applied. For multiple plumes, the methodology includes variation of the merging patterns and of the wake effects from tower housings for different wind directions. The main advantage to this model over previous models is its advanced theoretical development and extensive model validation with experimental data for its component submodels. From studies in the United States of America and Europe, an extensive database on cooling tower plumes and drift was accumulated and analysed to assist in the identification of superior theoretical assumptions. Other data, not used in model development, provided for independent model verification. The validation of each submodel is presented, and typical results are given for a representative natural-draft cooling tower installation and for a typical linear mechanical-draft cooling tower arrangement.

Spread-spectrum path diversity in a shadowed Rician fading land-mobile satellite channel

The effects of two types of path diversity techniques, namely selection diversity and maximal ratio combining, on the bit error probability are investigated for direct-sequence spread-spectrum (DS/SS) transmission in a land mobile satellite channel using coherent binary phase-shift keying (BPSK) modulation. It is assumed that the channel consists of a log-normally shadowed line-of-sight signal plus Rayleigh distributed multipath signals. The bit error probability is evaluated for light, average, and heavy shadowing. The performance is also measured in terms of the outage probability. >